The Required Time of Arrival (RTA) function of an aircraft is activated when the pilot sets a required time of arrival at a target waypoint ahead. The RTA function then predicts a trajectory that satisfies the time constraint and modifies the flight speeds accordingly. If the flight is in cruise phase and the target waypoint is in the descent phase, a conventional RTA function does not alter current cruise speed and scheduled descent speed independently.
Cruise speed and descent speed, and more particularly cruise Mach speed and descent calibrated air speed (CAS), are the two main search variables to find trajectories that comply with the RTA constraint. However, conventional RTA functions iterate over a Cost Index (CI) of the aircraft, which couples cruise Mach and descent CAS variations. In other words, conventional RTA functions iterate over a single variable, the CI, to find the trajectory. Each CI defines a unique Mach/CAS combination, given the aircraft cruise altitude, aircraft weight, and meteorological conditions. The CI is used for the initial trajectory prediction as well as for speed corrections during the flight.
A given CI implies a balance between fuel and operational costs. For CI=0, the minimum-fuel trajectory is taken without consideration of operational costs. As the CI increases, flight speeds increase too and, consequently, fuel costs become higher while flight time is reduced.
However, using CI-coupled Mach/CAS combinations often leads to solutions that are far from desirable because the resulting descent CAS or cruise Mach may be very close (or equal) to the aircraft speed limits. In general, the RTA function requires adjusting flight speeds during the flight and, if the initially specified speeds are too close to the aircraft speed limits, the RTA may become unachievable. Further, the resulting descent CAS or cruise Mach combinations may not result in the most fuel-efficient flight.